Performance Bounds on the Security of Transform-Based Analog Encryption
Theodoros Tsiligkaridis · 2017
We consider the problem of analog encryption without bandwidth expansion. The encryption method is based on a transform domain mapping and encrypting via a secret key, which effectively scrambles the transform coefficients. The intended receiver may decrypt the data using knowledge of the key. For finite-alphabet signals, such as communication signals, an adversary may be able to infer the key and decrypt the data. We derive bounds on the probability of correct key recovery and the mean waiting time for correct recovery, by making a connection with the coupon collector problem. Using a concentration inequality approach, we further derive finite sample bounds on the upper tail of the waiting time distribution for correct key recovery. These bounds allow us to predict how many frames the adversary needs to see in order to recover the key. The encryption methodology is finally applied to digital communication signals.